Paul Bowles ~ Scientific Research Laboratory Ford Motor Company

Proceedings of the American Control Conference Chicago, Illinois June 2000 Energy Management in a Parallel Hybrid Electric Vehicle With a Continuously Variable Transmission Paul Bowles ~ Scientific Research Laboratory Ford Motor Company Huei Peng Department of Mechanical Engineering and Applied Mechanics University of Michigan Xianjie Zhang Scientific Research Laboratory Ford Motor Company 1. Abstract This paper describes a control strategy for the energy management of a post-transmission parallel hybrid electric vehicle (PHEV) equipped with a continuously variable transmission (CVT). Results are presented highlighting the dynamic behavior of the model, as well as the fuel consumption normalized to a base case. A dynamic, forward simulation of a complete compact class vehicle including driver model and computer controller was written in Matlab / Simulink. Modeled vehicle components include: internal combustion engine, engine clutch, CVT, electric motor, lead-acid battery, vehicle driveline, hydraulic brakes, and the vehicle and tire dynamics. 2. Introduction Hybrid Electric Vehicles (HEVs) offer the potential to considerably increase the fuel economy of a vehicle, while reducing the overall emissions of a conventional powertrain [3]. Parallel Hybrid Electric Vehicles (PHEV) are HEVs configured such that the electric motor powertrain and the conventional powertrain can provide tractive power to the drive wheels simultaneously [2]. A Continuously Variable Transmission (CVT) provides an infinite number of transmission gear ratios within the limits of the device. This is in contrast to an automatic or manual transmission that typically offers between four and six gear choices. CVTs offer the same potential as the PHEV to increase the fuel economy of a vehicle while minimizing emissions [4]. It therefore makes sense to combine PHEV and CVT technology into a single vehicle. The combining of two different power sources in an PHEV implies that a strategy is necessary for regulating power flow in the vehicle [1]. The issue of energy management is discussed and an appropriate strategy is presented. The simulation model used in this paper is a dynamic, modular, forward-type simulation. That is the model consists of a driver sub-model trying to follow a predetermined velocity profile, a dynamic vehicle model, and a PHEV control module that essentially acts as the interface between the driver and vehicle models. The relationships between these components are shown in Figure 1. The PHEV control module controls the vehicle such that the driver power demands are met, while minimizing fuel consumption. The simulation was implemented in the Matlab / Simulink environment. [ Vehicle Driver EL Model ~ Control Module Dynamic Model ~ Computer ~ ~ PHEV with CUT I Figure 1: Major Model Components 3. Energy Management in a Post-Transmission PHEV with CVT Figure 2 shows a post-transmission PHEV and the possible sources of wheel motive power. Power can be supplied by the engine, the motor, or by both at the same time. l Paul Bowles was a graduate student in Mechanical Engineering at the University of Michigan during the completion of this work. 0-7803-5519-9/00 $10.00 2000 AACC 55

Power from en~ir~ ~ ~ ~mm~_~ Figure 2: PHEV Motive Power Sources When discussing the issue of PHEV power management, it is important to note that all of the vehicle's power ultimately comes from fuel. The battery is recharged by using the electric motor as a generator, thus transforming mechanical power into electrical power. In theory, the battery could also be recharged by somehow plugging the vehicle into a wall outlet. In practice, requiring consumers to do this would make the PHEV a very tough sell for automakers, so it is assumed that this is never done. Regenerative braking involves recapturing some of the energy normally lost through the hydraulic brakes. This energy is only available for storage because the vehicle was first put in motion by the engine/motor power plant. Figure 3 shows the two methods of recharging the battery. ~[~~ TRANSMISSION Direct loading t~ engine Figure 3: Battery Recharging Paths The HEV control problem can be summarized as follows. Assuming that the motive power demand (from the driver) must be met, and that certain driveability requirements must also be considered, how do we balance the power from the engine and from the motor? Also, knowing that the motor is powered by a battery that is charged by one of the two methods shown in Figure 3, when is regenerative braking to be used, and when should the engine be loaded to charge the battery? The answer to the question of when regenerative braking should be used is relatively straightforward. Assuming that there exists the capacity in the battery to store the energy, we would want to use regenerative braking as much as possible. Whatever energy is not recaptured is essentially wasted by using the hydraulic brakes. The real power management problem is whether to route power from the engine directly to the wheels or store it temporarily in the battery for use at a later time. These two power paths are shown in Figure 4, ignoring the possibility of regenerative braking. Po~.r from engine ~oted temporarily in batlc~y Figure 4: Possible Power Paths from Engine to Wheels Looking at Figure 4, it should be clear that converting the mechanical energy at the driveline into electric energy and again into chemical energy for storage, only to repeat the process in reverse, is significantly less efficient than allowing the power to flow directly from the engine to the wheels. We must keep in mind, however, that the energy stored in the battery is available for use at any time, and that the operating conditions under which the energy is stored may not be the same as the conditions under which the energy is released. This is particularly useful under the two following conditions: 1. During start-up or at slow speeds, when the engine cannot be operated at an efficient point, and; 2. When the driver power demand is so high that the engine is unable to meet it and the electric motor is required to provide additional torque. In other words, we wish to route power to the battery for use either when the engine cannot be operated efficiently or cannot meet the driver power demand. This allows both the engine and motor to be sized smaller than would be necessary if either one had to supply the entire vehicle's power directly. We also wish to recapture as much energy as possible through regenerative braking, as this energy is essentially free. 4. Energy Extraction from the Engine / CVT From Figure 4, we see that the power flow through the engine and CVT is unidirectional. While the engine and CVT friction can be used to brake the vehicle, no mechanical energy can be converted back into gasoline. Furthermore, the CVT gives us an additional degree of freedom over a conventional transmission to exactly choose the transmission gear ratio. This is in contrast to a manual or automatic transmission where the choice of gear ratio is limited to the number of gears, generally four or five. This implies that we have two degrees of freedom to control the amount of power that is delivered to the wheels from the engine / CVT part of the vehicle: the engine throttle angle and the CVT gear ratio. If we have two degrees of freedom in the control of the engine / CVT, then it should be possible to minimize one quantity (e.g. fuel consumption) subject to one constraint (e.g. the vehicle or driveshaft speed). Both of these facts set up the following optimization sub-problem. How can we maximize fuel efficiency 56

(minimize fuel consumption) subject to the following constraints: 1. The engine / CVT subsystem delivers the power requested by the PHEV controller. 2. The engine is operated within its operating limits. 3. The CVT is operated within its operating limits. This problem is complicated by the fact that the driveline speed (CVT output speed) cannot be controlled by the engine / CVT subsystem. The goal is to determine what engine throttle angle and CVT gear ratio should be used to minimize fuel consumption while producing a given amount of power at a known vehicle (or driveline) speed. Fuel minimization is accomplished by processing the steady-state engine fuel consumption map along with the torque loss data for the CVT. For a given vehicle speed and desired power output, we calculate the solution to the aforementioned optimization problem, assuming such a solution exists. If a solution does not exist, this simply means that we have reached the limitations of this vehicle. After this process is complete for the entire operating space (desired power versus speed) we have two maps. One map is the desired engine throttle angle required to minimize fuel consumption while delivering a certain amount of power to the driveline at a given vehicle speed. The second map is similar but contains the corresponding CVT gear ratio that minimizes fuel consumption. The CVT gear ratio and engine throttle angle maps are shown in the following figures. The CVT gear ratio range is approximately 0.5 through 2.5. Best Case CVT Gear Ratio! Stars In~c~e Maxi aura Pow4 Cur',e li =j '...... -..t.5 i ~ "... ~../-~.t='t'~ "~=7-q -...... (--~; 10 20 30 40 50 60 70 Vehicle Speed (MPH) Figure 5: CVT Gear Ratio Curves for Minimum Fuel Consumption ifl01 Best Case Engine Thr~tle Angle (deg) [ St_.~Lln~!ate M~i~ Jm P we"dd~'lr'e._ I... [... w:,.r:. 10 20 30 40 50 60 70 Vehicle Speed (MPH) Figure 6: Engine Throttle Angle for Minimum Fuel Consumption The plot of the CVT gear ratio (Figure 5) provides some insight into the general behavior of the system. At low requested power levels, the best CVT gear ratio is quite low and gets lower as speed increases. While this may seem strange, it can be explained by the fact that the engine / CVT subsystem produces low levels of power most efficiently at low engine speeds. There is, however, a minimum engine speed below which it is not able to provide significant power; this limit is around 1000 rpm. In order to maintain a low engine speed as the vehicle speed increases, the CVT gear ratio must drop. At very low speeds (about 10 mph), the CVT must be operated at a gear ratio above two, as anything less could stall the engine. If we look at different levels of power output along the 25 mph line we notice the general trend that increasing the power output results in a higher gear ratio. This is because the engine produces high power more efficiently at high speeds. As the vehicle speed increases we hit the upper engine speed limit and consequently the gear ratio must drop to allow the engine to power the vehicle. Note that the engine / CVT can only produce power up to the maximum power curve. This curve is speed dependent. Should the driver power request be higher than the maximum power curve, the motor would have to assist the engine in meeting the demand. 5. Charge-Sustaining Strategy The charge-sustaining strategy implemented here is as follows. At low power levels, the motor provides all power to the vehicle. When the driver requested power crosses a preset threshold, the 'engine on power level', the engine is engaged and replaces the motor in powering the vehicle. Should the power request rise above the maximum power that the engine / CVT is able to deliver, the motor is again called upon to deliver the difference in power up to its capacity. When the battery state of charge 57

_ falls below a low limit, the vehicle attempts to charge the battery at a preset power, the 'recharge level'. The corresponding amount of power is added to the driver power request and is satisfied by the engine, if possible. 6. Drive Cyde Simulation Results and Discussion This section presents results obtained through simulation of the vehicle over a Federal Urban Drive Cycle (FUDS) cycle. Figure 7 and Figure 8 show the dynamic simulation response when the 'engine on power level' is set to 15kW and the battery rate of recharge is set to 30kW. The traces shown in Figure 7 are vehicle speed (mph), vehicle speed error (m/see), driver accelerator pedal (% of max), engine power requested (kw) and motor power requested (kw). In Figure 8, the traces shown are battery state of charge (%), brake line pressure (psi), regenerative braking power (kw), CVT gear ratio and battery terminal voltage (V). FUDS Cycle Data - 1 601 IF'.',, } [ l I [... Aehml II 40~,- - - - ~. -T,.... ~.......... : cc _._ 2 --- '--- ' -- i--- ~--- i- - ' - - LU I........ t- - - # 0 o ago 4oo 69o ~9o lqoo lg~o ~ 5oL ~J_ a ~_.... ~.... ±.... =.... J _ J [ 0 J...... J-hi..... 0 ~0 490 690 800 1000 1200 "rime (s) Figure 7: FUDS Results 1 FUOS Cyete Osia -2 70/ ] I I l I [ / 55 I I I I I I I I 30(] J:it:tt -... t't.... 0 200 400 60O 800 1000 1200 / i. ; i i ; i i 20 - - - 4 - - ~ - --I- +.... I.... -4--- ~o aq 2oo 4oo 600 Boo,ooo 1~oo, ~, a~h~---li~ ~_tu, ov_l_u ~ ', ~,, ' OOI m t I J t 4000 2@ z~o 66,00 600 10(')0 12,00 > 350.~. I.. I..,. I I m 250 t t I r I I I J "nine (s) Figure 8: FUDS Results 2 Vehicle speed was controlled by the driver model to within 2m/s. The commanded motor power trace shows both positive and negative values, highlighting its motoring and regenerative functions. Negative values in this trace represent both regenerative braking (shown as positive in Figure 8), as well as additional charging of the battery. The battery high and low state of charge limits were set to 65% and 60% respectively. This was done to ensure that there would be several charging and discharging periods over a single FUDS cycle, which aid in fuel economy comparisons (see Appendix). In practice, a larger battery state of charge range would be used, allowing the vehicle to be driven at low power levels for a longer period of time without recharging the battery. A wider range in state of charge limits also means that the vehicle has greater range at zero emissions (with the engine off). Despite these facts, restricting the battery state of charge to a narrow range does not inhibit us from observing the benefits of hybridization as well as changes in the control strategy set points. Table 1 contains a summary of the normalized fuel economies obtained through many such dynamic simulations. The 'engine on' power levels were chosen to avoid engine operation in its inefficient range. Three rates of recharge were investigated. The simulation without a normalized miles/gallon rating was not able to maintain the battery state of charge. Having an engine on power level of 20kW consumed so much battery energy that a 10kW rate of recharge was unable to sustain the charge over a FUDS cycle. Table 1: FUDS Fuel Economy Comparisons FUDS Cycle Normalized Miles/Gallon Results Recharge Level (kw) Engine On Power Level (kw) Engine Only 11 FUDS Cycle Normalized MPG 1.00 1.69 N/A 10 11 15 1.71 11 30 1.74 15 10 1.73 15 15 1.68 15 30 1.81 20 10 N/A (SOC didn't recover) 20 15 1.67 20 30 1.76 The observed normalized hybrid fuel economy was relatively insensitive to the changes in engine on power level and recharge level. This assumes that the recharge level was matched appropriately with the engine on power level to maintain the battery state of charge (not the case for 20kW engine on level and 10 kw recharge). The results imply that most of the benefits of hybridization 58

occur at low engine on power levels. This means two things: 1. A major benefit of hybridization is regenerative braking, which is the same for all of the hybrid cases and non-existent for the engine only case. 2. The process of altering the power path from that of a conventional vehicle to temporarily storing energy in the battery is most beneficial at low power levels (less than 1 lkw). Recall that in the HEV presented here, all of the vehicle's power ultimately comes from the engine. Furthermore, the HEV is an incremental change from the conventional vehicle. There is therefore an inherent limitation in the achievable fuel economy of the HEV; that limit is the maximum fuel economy of the engine coupled with the corresponding losses in the rest of the vehicle. In light of this, it has been shown that the two major benefits of post-transmission, parallel hybridization are the ability to recapture energy through regenerative braking and the ability to avoid low power, inefficient engine operation. 7. References [1] Biscarri, Erbis L., Tamor, M.A. and Murtuza, Syed, "Simulation of Hybrid Electric Vehicles with Emphasis on Fuel Economy Estimation," International Congress and Exposition. SAE Technical Paper 981132. 1998. [2] Powell, B.K., Bailey, K.E., and Cikanek, S.R., "Dynamic Modeling and Control of Hybrid Electric Vehicle Powertrain Systems", IEEE Control Systems Magazine, pp 17-33, October 1998. [3] Powell, B.K. and Pilutti, T.E., "A Range Extender Hybrid Electric Vehicle Dynamic Model", Proceedings of the 33 rd IEEE Conference on Decision and Control, Lake Buena Vista, FL, December 1994. [4] Sakaguchi, S., Kimura, E. and Yamamoto, K., "Development of an Engine-CVT Integrated Control System." SAE Technical Paper 1999-01-0754. 8. Appendix - HEV Fuel Economy Calculation distance traveled by the vehicle and divide by the amount of fuel consumed in traveling that distance. Hybrid electric vehicles are more complicated, however, as the possibility of energy storage in the battery is introduced. The problem can be illustrated with a simple example. Suppose we wish to evaluate the fuel economy of a vehicle with a certain control strategy over a drive cycle such as the FUDS, and that the initial battery state of charge is 70%. Suppose that at the end of the FUDS, the vehicle has consumed 0.30 gallons of fuel and has a final battery state of charge of 68%. If we simply divide the distance traveled by the fuel consumed, we will overstate the fuel economy, as the depletion of the battery has not been factored in. To overcome this problem, two identical drive cycles were run in succession. Then, a window of time equal to the length of a FUDS cycle was 'slid' along the time axis until the battery state of charge at the start and end of the sliding window cycle were equal. So long as the control strategy keeps the state of charge between two boundaries, eventually a point in the 'double cycle' will be reached where the starting and ending battery states of charge are equal. This is shown in Figure 9. Within the shifted window, the vehicle has still traveled through a complete FUDS cycle. We can therefore divide the distance traveled within the window by the fuel consumed without regard for the battery state of charge. By doing this, we are forcing the vehicle to be in a charging mode at the beginning of the shifted cycle and a discharging mode at the end (or vice versa). Consequently, the vehicle is not in exactly the same state at the start and end of the shifted cycle, but it is similar enough to be used as an approximation. Original F lr)~ Battery SOC over Two FUDS Cycles 6~....,,,4k:-... %" 5oo ~ooo ~soo 2oo0 2;00 Time (s) Figure 9: Shifted FUDS Time Window In a conventional vehicle, calculation of the fuel economy is straightforward. One simply takes the 59